Advertisement

Approximations of the nonlinear filter by periodic sampling and quantization

  • H. Korezlioglu
  • G. Mazziotto
Session 10 Filtering
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)

Abstract

Exact filtering algorithms are given and approxination rates are computed for various approximations of the nonlinear filter via periodic sampling and quantization of the observation process.

Keywords

Markov Process Stochastic Differential Equation Observation Process Nonlinear Filter Transition Semi 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    K.J. ASTRÖM: Optimal control of Markov processes with incomplete state information; J. Math. Anal. and Appl. 10, 174–205 (1965).Google Scholar
  2. (2).
    G.B. DI MASI and W.J. RUNGGALDIER: Approximations and bounds for discrete-time filtering; Preprint (1982).Google Scholar
  3. (3).
    I.I. GIKHMAN and A.V. SKOROKHOD: Stochastic differential equations; Springer-Verlag (1972).Google Scholar
  4. (4).
    G. KALLIANPUR and C. STRIEBEL: Estimation of stochastic systems; Ann. Math. Stat. 39, 785–801 (1968).Google Scholar
  5. (5).
    H.J. KUSHNER: Probability methods for approximations in stochastic control and for elliptic equations; Academic Press (1977).Google Scholar
  6. (6).
    R.S. LIPTSER and A.N. SHIRYAYEV: Statistics of random processes 1: General theory; Springer-Verlag (1977).Google Scholar
  7. (7).
    J.T. LO: Optimal nonlinear estimation-Part 2: Discrete observation; Information Sc. 7, 1–10 (1974).Google Scholar
  8. (8).
    J. NEVEU: Martingales à temps discret; Masson (1972).Google Scholar
  9. (9).
    E. PARDOUX and D. TALAY: Discretization and simulation of stochastic differential equation, to be published in Acta Applicande Mathematica.Google Scholar
  10. (10).
    J. PICARD: Approximation of nonlinear filtering problems and order of convergence; Lect. Notes in Control and Inf. Sc. 61, Springer-Verlag (1984).Google Scholar
  11. (11).
    E. PLATEN: Approximation of Ito integral equations; Lect. Notes in Control and Inf. Sc. 28, 172–176, Springer-Verlag (1980).Google Scholar
  12. (12).
    E. PLATEN: Approximation method for a class of Ito processes; Lietuvos Kat. Rinkinys XXI-1, 121–133 (1981).Google Scholar
  13. (13).
    Y. TAKEUCHI and H. AKASHI: Nonlinear filtering formulas for discrete time observations: SIAM J. Control and Opt. 12-2; 244–261 (1981).Google Scholar
  14. (14).
    M. ZAKAI: On the optimal filtering of diffusion processes; Z. Wahr. V. Geb. 11, 230–249 (1969).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • H. Korezlioglu
    • 1
    • 2
  • G. Mazziotto
    • 1
    • 2
  1. 1.Dpt Systèmes et CommunicationsE.N.S.T.Paris Cedex 13
  2. 2.PAA/TIM/MTI C.N.E.T.Issy Les Moulineaux

Personalised recommendations